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 Title: Convergence in Ergodic Theory Author(s): Argiris, Georgios Doctoral Committee Chair(s): Rosenblatt, Joseph Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: We investigate two problems involving convergence in ergodic theory. The first problem is the following: Given a measure preserving transformation T and a weight function w(alpha) → 0 as alpha → 0, is there a p > 0 such that the expression w(alpha)#{ n : 1n k=1nfT kx >a } have a limit, a.s. or in norm, as alpha → 0 for all functions f ∈ Lp0 [0,1]? No, we show. Here # denotes counting measure and f's are taken to be mean-zero functions. We also consider similar questions for the more general operator w(alpha)#{n : 1nq k=1n f(Tk(x)) > alpha}, q > 1. The second problem addressed is to give arithmetic and probabilistic characterizations on the integer sequence ( nk) such that the series of ergodic differences k=1infinity ( Ank+1f-Ankf ), where An denotes the usual ergodic averages, converges unconditionally for all functions f in some Lp space. Issue Date: 2001 Type: Text Language: English Description: 51 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. URI: http://hdl.handle.net/2142/86781 Other Identifier(s): (MiAaPQ)AAI3023009 Date Available in IDEALS: 2015-09-28 Date Deposited: 2001
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